Fill in the gaps below:​

Since 2704 = 2⁴ × 13², we need [tex]m = 13[/tex] and [tex]n=2[/tex], since this gives

[tex]\dfrac{2704m}n = \dfrac{2^4 \times 13^2 \times 13}2 = 2^3 \times 13^3 = 26^3[/tex]

The values of m and n that make 2704 × m/n a perfect cube are:

m = 13 and n = 2.

We have,

We can start by factoring 2704, which is 52².

So we have:

= 2704 × m/n

= 52² × m/n

= (2² × 13²) × m/n

For the expression to be a perfect cube, we need all the prime factors to appear in groups of three.

Since 2 and 13 appear only once each, we need to find another factor that appears twice.

Since m and n are both prime, and the fraction m/n is simplified, there are only two possible values for m and n:

m = 2 and n = 13, or

m = 13 and n = 2

Let's try the first case:

2704 × m/n = 2704 × 2/13 = 416

416 is not a perfect cube, so this case does not work.

Now let's try the second case:

2704 × m/n = 2704 × 13/2 = 17696

17696 is 28³, which is a perfect cube.

Therefore,

The values of m and n that make 2704 × m/n a perfect cube are:

m = 13 and n = 2.

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The value of p is -1 in the given equation of of parabola.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point called focus and a line called the directrix.

Equation for a Parabola

The general formula or the equation for representing a parabola is given by,

y² = 4px

Here,  (h,k) being the vertex of the parabola,

y = a(x-h)² + k

x = b(y-k)² + h

The focus of this parabola is given by (p, 0).

The directrix of the parabola is the line drawn perpendicular to the y-axis and traversing the point (-p, 0). The directrix is parallel to the parabola's axis.

What is the value of p in the equation for parabola?

The given equation is,

y² = -4x

Comparing this equation with the general formula of the parabola, we get,

p = -1

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Answer:

B. 20

Step-by-step explanation:

Cos a = b/c

Cos 53° = b/25

b = 25 × 0,6 = 15

x = √(25² - 15²)

x = √(625 - 225)

x = √400

x = 20

The required algebraic expression is Y = 3X + 2

This table describe the  relation between x and y

x =  2  3    4   5      

y =  8  11   14  17

Alegebraic expression consists of constant and variable. eg x, y, z etc.

As the data given in the table, we conclude that:

1) The difference in the values of y is 3.

2) When we multiply this difference by x and add 2 it gives the next value of y.

so the from above discussion Y = 3X + 2

Thus, The required algebraic expression is  Y = 3X + 2

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Based on the information, it can be inferred that Carl's house is 6 blocks from Ann's house.

To identify where each friend's house is, we must graph the information provided as shown below.

Once we have made the graph we will identify that Carl's house is 6 blocks east of Ann's house.

Note: This question is incomplete because there is some information missing. Here is the missing information:

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The solution of the equation is 5477x + 12y = -56

Given the equation;

-8 -48-4y-8y = -x + 5480x

First, we collect like terms

-56 - 12y = 5477x

Collect the numbers with variables together

-56 = 5477x + 12y

Thus, the solution of the equation is 5477x + 12y = -56

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Answer:

[tex](x-5)^2+(y+4)^2=100[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given:

Substitute the given values into the circle equation and solve for r:

[tex]\implies r^2=(-3-5)^2+(2-(-4))^2[/tex]

[tex]\implies r^2=(-8)^2+(6)^2[/tex]

[tex]\implies r^2=64+36[/tex]

[tex]\implies r^2=100[/tex]

[tex]\implies r=\sqrt{100}[/tex]

[tex]\implies r=10[/tex]

Substitute the given center and the found value of r into the circle equation to create the equation of the circle:

[tex]\implies (x-5)^2+(y-(-4))^2=10^2[/tex]

[tex]\implies (x-5)^2+(y+4)^2=100[/tex]

Answer:B 1/2

I can't type math symbols well in BRAINLY, so I use pictures╯﹏╰

Answer:

A. 1

Step-by-step explanation:

18-4x=7x+7

Use this equation to find x.

Simplify.

18-4x=7x+7

Subtract 7 from both sides.

11-4x=7x

Add 4x to both sides.

11=11x

Divide 11 from both sides.

x=1

Hope this helps!

Answer:

-5 u + 1 v = (-16)

12 u - 1v = 48

adding,

7 u = 32

V = (-16) + 5(32/7)

V = (-16) +160/7

V = -112 + 160/7

the length of the shorter side is:L  = 13.125cm

In the longer side we have 8 segments.

We know that the side measures 35 cm, then each one of the 8 segments measures:

35cm/8 = 4.375cm

Now, we can see that in the shorter side we have 3 of these segments.

Then the length of the shorter side is:

L  = 3*(4.375cm) = 13.125cm

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The angle between the lines joining the origin to the points of intersection of the degenerated elipse and the straight line is approximately 136.635°.

We have the graphs of a degenerated ellipse and a line, which intercept each other at points (x₁, y₁) = (-0.293, 1.121) and (x₂, y₂) = (- 1.707, - 3.121). A representation of the situation is shown in the image attached below.

Now we find the angle between the two lines by dot product:

[tex]\cos \theta = \frac{(- 0.293, 1.121)\,\bullet \,(- 1.707, - 3.121)}{1.159 \,\cdot\, 3.557}[/tex]

[tex]\cos \theta = - 0.727[/tex]

θ ≈ 136.635°

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Answer:

a horizontal line is graphed

Step-by-step explanation:

It does not change it will always stay at the same y but just different x.
The rate of change/slope is the change in y divided by a corresponding change in x.

Hi. . .

A, and D.

Cause- A, and D do not show the constant rate of the change.

Hope It Helps . . .

The number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

The zero of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

In other words, The zeros of a polynomial p(x) are the values of x which satisfy the equation p(x) = 0

For example, the zero of the polynomial f(x) = x³- 12x²+ 20x is  x = 0 or x = 10 or x = 2.

This is because f(x) = o when we substitute those x values.

Therefore, the number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

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Answer:

x = 17deg

Step-by-step explanation:

Let angle y be the unknown angle IN THE TRIANGLE.

Angle y = 180 - 90 - 73

= 17deg

Angle x = Angle y (Alternate angles on 2 parallel lines)

Angle x = 17 deg

Answer:

17° is the answer.

Answer:

3/20

decimal form: 0.15

It is proved in the answer that an exterior angle of the triangle equals the sum of two opposite interior angles.

If a triangle's side is created, the outside angle that results is equal to the product of the two opposite internal angles.

In the figure given below we can see:

∠BCD is the exterior angle of the triangle

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum property of a triangle)

∠BCA + ∠BCD = 180°(Linear pair)

From both equations we can say that:

∠ABC + ∠BAC + ∠BCA  = ∠BCA + ∠BCD

∠ABC + ∠BAC = ∠BCD

Hence Proved

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Answer:

A. The sloped graph doesn't represent the verbal description because the slope is 1 hot dog per 4 min

Step-by-step explanation:

B. Option b is valid response of the verbal description because the statements say Katie starts with 3 bonus hotdogs and then eats 4 hotdogs/min. This is the slope-int of the verbal description.

C. &D. When you substitute the table values of x into the slope-int equation, you should get the y-values listed in the table

Hope it helps!

Answer: I thin The first one 2r+3r+9

Step-by-step explanation: Because he scored a number of 2 port shots which means he scored more than one but the 9 points is just 9 points from free throws which gives only 1 point each and 3 port shots and much as 2 point shots so 3r also

2r+3r+ just 9

The inequality equation of the lines are given as x + 2y ≤ 5 and 3x + y ≤ 4. Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The graph is given below.

From the graph, equation of the lines are given as

x + 2y = 5 and 3x + y = 4

But for the inequality is shown in the graph. Then the inequality equation of the lines are given as

x + 2y ≤ 5 and 3x + y ≤ 4

Then the correct option is C.

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Answer:

S = {2, 2, 5, 5, 11}

Step-by-step explanation:

So you can partially build a data set given this information. There is going to be 5 positive numbers and the median is going to be 5 so the data set is going to have 5 in the middle which should look like this

S = {a, b, 5, c, d} where a, b, c, d are the other values. Since it has a mode of 2 and 5 that means that the occurrences of 2 and 5 will be equal, otherwise it would only have 1 mode. and they have to appear at least twice since if they only appeared once, there would either be another mode, or the data set would have 5 modes.

So the data set is going to look like this

S = {2, 2, 5, 5, d}

Now the only thing left to do is calculate d. This is where you use the mean to determine the last value. The mean can be calculated as

(the sum of the data set) / (the amount of values in the data set)

Since we know the mean you can set up an equation to find the value of d

[tex]5 = \frac{2+2+5+5+d}{5}\\5=\frac{14+d}{5}\\25=14+d\\11=d[/tex]

so the last value is 11. This gives you the complete data set of 5 positive integers

S = {2, 2, 5, 5, 11}

The expression of function g(x) is [tex]|\frac {x - 1}2| + 3[/tex]

The function is given as:

[tex]f(x) = |x|[/tex]

When the function is compressed horizontally by a factor of 2, the rule is:

f'(x) = f(x/2)

So, we have:

[tex]f(x) = |\frac x2|[/tex]

When the function is shifted left by 1 unit, the rule is:

f"(x) = f(x + 1)

So, we have:

[tex]f'(x) = |\frac {x - 1}2|[/tex]

When the function is shifted up by 3 units, the rule is:

g(x) = f"(x) + 3

So, we have:

[tex]g(x) = |\frac {x - 1}2| + 3[/tex]

Hence, the expression of function g(x) is [tex]|\frac {x - 1}2| + 3[/tex]

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Answer:

Step-by-step explanation:

Comment

When you join 2 consecutive midpoints with a line between them, the length of that line is 1/2 the length of the side opposite the line you just drew.

In other words 24 is 1/2 the length of yz.

Solution

1/2 yz = AB

AB = 24

1/2 yz = 24                 Multiply both sides by 2

2(1/2 yz) = 2*24

yz = 48

Answer

yz = 48

Answer: 0.3, [tex]\frac{6}{20}[/tex], [tex]\frac{3}{10}[/tex], 30%

Step-by-step explanation:

    We will divide wanted outcomes by possible outcomes.

          [tex]\displaystyle \frac{\text{wanted outcomes, green cubes}}{\text{possible outcomes, cubes in bag}} =\frac{6}{20}[/tex]

    Now, we will find four values equivalent to [tex]\frac{6}{20}[/tex]. See attached.

T probability of rolling doubles after 45 tosses is 0.156

To do this, we enter the data values in a graphing calculator.

From graphing calculator, we have the following summary:

The regression equation is

y = bx + a

Where

b = SP/SSX = 1375/8250 = 0.16667

a = MY - bMX = 8.7 - (0.17*55) = -0.46667

So, we have:

y = 0.16667x - 0.46667

Approximate

y = 0.167x - 0.467

When the number of tosses is 45, we have:

y = 0.167 * 45 - 0.467

Evaluate

y = 7.048

Approximate

y = 7

45 tosses gives 7 doubles.

So, the probability is:

P = 7/45

Evaluate

P = 0.156

Hence, the probability of rolling doubles after 45 tosses is 0.156

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Answer:

$80,000

Step-by-step explanation:

Define the variables:

Let x =  "fish-flavored" chicken company investment (in dollars)

Let y = spray-on vitamins company investment (in dollars)

If Allen invested a total of $100,000:

⇒ x + y = 100000

Given:

⇒ 0.03x + 0.01y = 2600

Rewrite the first equation to make y the subject:

⇒ y = 100000 - x

Substitute into the second equation and solve for x:

⇒ 0.03x + 0.01(100000 - x) = 2600

⇒ 0.03x + 1000 - 0.01x = 2600

⇒ 0.02x + 1000 = 2600

⇒ 0.02x = 1600

⇒ x = 80000

Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.

Answer:

PART A:

The range, the IQR (inter-quartile range) and the standard deviations are measures which are used to measure the spread of a data set.

A dataset is more consistent relative to another data set when the standard deviation is less than that of the other data set.

From the table, it can be seen that Team C has the least standard deviation.

Therefore, If the club wants to award the team that has the most consistent scoring among its team members, team C should be chosen.

PART B

The mean and the median is a measure of center of a data set.

The mean describes the average of a data set.

From the table, it can be seen that Team B has the highest average score.

Therefore, If the club wants to award the team with the highest average score, team B should be chosen.

The median in the box plot is: 31

Q1 (lower quartile) = 26

The median is the value at the vertical line that divides the box.

The Q1 (lower quartile) is the value at the beginning of the edge of the box.

Thus, from the given box plot, we have the following:

Median = 31

Q1 (lower quartile) = 26

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Answer:

26542%

Step-by-step explanation:

12,209,400/46,000 = 265.421

265.421 × 100 ≈ 26542%